As long as there is a Stay in the Supreme Court regarding the upper age limit, you will be eligible for NEET. We want you to read this. This is an excerpt from the  NTAInformation Bulletin. It says:

"The upper age limit of 25 years as prescribed under the Regulations on Graduate Medical Education, 1997 vide amendment dated 22.01.2018, was challenged before the Hon'ble High Court of Delhi and the said upper age limit had been upheld vide judgement dated 11.05.2018 in W.P. No.1813/2018 & other connected matters. The said judgement dated 11.05.2018 was challenged before the Hon'ble Supreme Court of India in SLP (C) No. 14320/2018 & other connected matters, when vide interim order dated 29.11.2018, candidates who are 25 years and above were provisionally permitted to appear in NEET-UG-2019 subject to the final outcome of the said matters. The Supreme Court thereafter, vide order dated 29.04.2019 had permitted the candidates to appear provisionally in the Counselling subject to the adjudication o f the matters. The aforesaid matters are pending adjudication before the Hon'ble Supreme Court of India and the authorities shall abide by any order that may be passed for NEET-UG-2020.

Thus, the candidates above 25 years are provisionally permitted to appear and their candidature is subject to the outcome of pending Petitions before the Hon'ble Supreme Court."

So you are still eligible to appear for NEET.